Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Pumpluen, Susanne"'
Autor:
Pumpluen, Susanne
We construct unital central nonassociative algebras over a field $F$ which have either an abelian Galois extensions $K/F$ or a central simple algebra over a separable extension of $F$ in their nucleus. We give conditions when these algebras are divis
Externí odkaz:
http://arxiv.org/abs/2407.16256
Autor:
Pumpluen, Susanne
We classify division algebras that are principal Albert isotopes of cyclic Galois field extensions of degree $n>2$ up to isomorphisms. We achieve a "tight" classification when the cyclic Galois field extensions is cubic. The classification is "tight"
Externí odkaz:
http://arxiv.org/abs/2407.11598
Autor:
Nevins, Monica, Pumpluen, Susanne
We determine and explicitly parametrize the isomorphism classes of nonassociative quaternion algebras over a field of characteristic different from two, as well as the isomorphism classes of nonassociative cyclic algebras of odd prime degree when the
Externí odkaz:
http://arxiv.org/abs/2406.11419
Autor:
Moran, Thomas, Pumpluen, Susanne
Let $F$ be a field of characteristic not 2 or 3. The first Tits construction is a well-known tripling process to construct separable cubic Jordan algebras, especially Albert algebras. We generalize the first Tits construction by choosing the scalar e
Externí odkaz:
http://arxiv.org/abs/2403.16342
Autor:
Pumpluen, Susanne
Nonassociative differential extensions are generalizations of associative differential extensions, either of a purely inseparable field extension $K$ of exponent one of a field $F$, $F$ of characteristic $p$, or of a central division algebra over a p
Externí odkaz:
http://arxiv.org/abs/2403.15914
Autor:
Pumpluen, Susanne
Witt rings for nondegenerate forms $\varphi$ of degree $d$ over a field of characteristic 0 or greater than $d$ were defined by Harrison and Pareigis. We revisit and discuss their definition as well as some special cases, classify the $H$-forms emplo
Externí odkaz:
http://arxiv.org/abs/2403.15287
Autor:
Owen, Adam, Pumpluen, Susanne
We find examples of polynomials $f\in D[t;\sigma,\delta]$ whose eigenring $\mathcal{E}(f)$ is a central simple algebra over the field $F = C \cap {\rm Fix}(\sigma) \cap {\rm Const}(\delta)$.
Externí odkaz:
http://arxiv.org/abs/2106.02423
Autor:
Thompson, Daniel, Pumpluen, Susanne
Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Using skew polynomials $f\in R$, we construct division algebras and a generalization of maximum rank distance codes consisting of ma
Externí odkaz:
http://arxiv.org/abs/2103.12691
Autor:
Pumpluen, Susanne, Thompson, Daniel
Let $D$ be a finite-dimensional division algebra over its center and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Under certain assumptions on $\delta$ and $\sigma$, the ring of central quotients $D(t;\sigma,\delta) = \{f/g \,|\, f \in D[t;\sigma,\
Externí odkaz:
http://arxiv.org/abs/2006.10418
Autor:
Owen, Adam, Pumpluen, Susanne
Let $K$ be a field and $\sigma$ an automorphism of $K$ of order $n$.Employing a nonassociative algebra, we study the eigenspace of a bounded skew polynomial $f\in K[t;\sigma]$. We mainly treat the case that $K/F$ is a cyclic field extension of degree
Externí odkaz:
http://arxiv.org/abs/1909.07728